Why is Godel's first theorem not a proof for the truth of the so called undecidable proposition? You may say it's a proof from the outside, but if not all proofs from the outside be formalized inside the system then the system is really not powerful.
Because by Tarski's undefinability of truth theorem one can not even define the truth of formulas of a strong enough system inside it (because it leads to the famous liar's paradox). You can say that the system is not "powerful", but then there is no reasonable "powerful" systems at all.
(One can say the same thing about any impossible thing but that is not a good argument, untenability to do an impossible thing is not a weakness.)